On massive cosmological scalar perturbations

Physical Review D, 2000

We study adiabatic (curvature) and entropy (isocurvature) perturbations produced during a period of cosmological inflation that is driven by multiple scalar fields with an arbitrary interaction potential. A local rotation in field space is performed to separate out the adiabatic and entropy modes. The resulting field equations show explicitly how on large scales entropy perturbations can source adiabatic perturbations if the background solution follows a curved trajectory in field space, and how adiabatic perturbations cannot source entropy perturbations in the long-wavelength limit. It is the effective mass of the entropy field that determines the amplitude of entropy perturbations during inflation. We present two applications of the equations. First, we show why one in general expects the adiabatic and entropy perturbations to be correlated at the end of inflation, and calculate the cross-correlation in the context of a double inflation model with two non-interacting fields. Second, we consider two-field preheating after inflation, examining conditions under which entropy perturbations can alter the large-scale curvature perturbation and showing how our new formalism has advantages in numerical stability when the background solution follows a non-trivial trajectory in field space.

Physical Review D, 1996

We study the metric perturbations produced during inflation in models with two scalar fields evolving simultaneously. In particular, we emphasize how the large-scale curvature perturbation ζ on fixed energy density hypersurfaces may not be conserved in general for multiple field inflation due to the presence of entropy as well as adiabatic fluctuations. We show that the usual method of solving the linearized perturbation equations is equivalent to the recently proposed analysis of Sasaki and Stewart in terms of the perturbed expansion along neighboring trajectories in field-space. In the case of a separable potential it is possible to compute in the slow-roll approximation the spectrum of density perturbations and gravitational waves at the end of inflation. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and ζ is conserved.

Physics Letters B, 2016

We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δP nad , another is for a general matter field δP c,nad , and the last one is valid only on superhorizon scales. The first two definitions coincide if c 2 s = c 2 w where cs is the propagation speed of the perturbation, while c 2 w =Ṗ /ρ. Assuming the adiabaticity in the general sense, δP c,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δP nad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs = cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δP nad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw = cs, where δP nad = δP c,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.

Classical and Quantum Gravity, 1996

We further clarify how scalar metric perturbations are ampli ed in an in ationary cosmology. We rst construct a simple, analytic model of an inationary cosmology in which the expansion scale factor evolves continuously from an in ationary era to a radiation-dominated era. From this model, it is clear to see how scalar perturbations are ampli ed. Second, we examine the recent claims of Grishchuk, and the reply by Deruelle and Mukhanov, regarding the evolution of scalar perturbations through an abrupt transition in the equation of state of the cosmological uid. We demonstrate that the \standard results" regarding the ampli cation of scalar, density perturbations from in ation are valid.

Physical Review D, 1995

arXiv:gr-qc/9506050v1 23 Jun 1995 SUSSEX-AST-95/6-3, IEM- Abstract We show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of these models is the possibility that the curvature perturbations on super-horizon scales may not be constant due to non-adiabatic perturbations of the two fields. Within a given model, the tilt and relative amplitude of the scalar and tensor perturbation spectra gives constraints on the parameters of the gravity theory, which may be comparable with those from primordial nucleosynthesis and post-Newtonian experiments.

1996

We discuss metric perturbations produced during a period of inflation in the early universe where two scalar fields evolve. The final scalar perturbation spectrum can be calculated in terms of the perturbed expansion along neighbouring trajectories in field-space. In the usual single field case this is fixed by the values of the fields at horizon-crossing, but in the presence of more than one field there is no longer a unique slow-roll trajectory. The presence of entropy as well as adiabatic fluctuations means that the super-horizon-sized metric perturbation ζ may no longer be conserved and the evolution must be integrated along the whole of the subsequent trajectory. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and ζ is conserved.

Physics Reports, 2012

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f (R), general higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

Classical and Quantum Gravity, 2012

Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly introducing a timelike reference congruence. The common ground is the use of gauge invariants derived from the metric tensor, the stress-energy tensor, or from vectors associated with a reference congruence, as basic variables. Although there is a complication in that there is no unique choice of gauge invariants, we will show that this can be used to advantage.

Journal of Cosmology and Astroparticle Physics, 2005

We explain why it is so difficult and perhaps even impossible to increase the cosmological tensorto-scalar perturbation ratio during the post-inflationary evolution of the universe. Nevertheless, contrary to some recent claims, tensor perturbations can be relatively large in the simplest inflationary models which do not violate any rules of modern quantum field theory.

Physical Review D, 2012

We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small scale limit, and for the open FRW solution we repeat the analysis around the full background. We find that the perturbations display similar properties: the longitudinal modes of the massive graviton are instantaneous at quadratic level, but they acquire a kinetic term at cubic order.